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On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour
On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour
Department of Mathematical Sciences Faculty Publications
A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernoulli distribution with beta priors are given. Finally, some numerical results are presented.
Vertices Of Self-Similar Tiles, Da-Wen Deng, Sze-Man Ngai
Vertices Of Self-Similar Tiles, Da-Wen Deng, Sze-Man Ngai
Department of Mathematical Sciences Faculty Publications
The set Vn of n-vertices of a tile T in \Rd is the common intersection of T with at least n of its neighbors in a tiling determined by T. Motivated by the recent interest in the topological structure as well as the associated canonical number systems of self-similar tiles, we study the structure of Vn for general and strictly self-similar tiles. We show that if T is a general self-similar tile in \R2 whose interior consists of finitely many components, then any tile in any self-similar tiling generated by T has a finite …
Self-Similar Measures Associated To {Ifs} With Non-Uniform Contraction Ratios, Sze-Man Ngai, Yang Wang
Self-Similar Measures Associated To {Ifs} With Non-Uniform Contraction Ratios, Sze-Man Ngai, Yang Wang
Department of Mathematical Sciences Faculty Publications
In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, Peres, et al.